Additive manufacturing (AM) is poised to bring about a revolution in the way products are designed, manufactured, and distributed to end users. This technology has gained significant academic as well ...as industry interest due to its ability to create complex geometries with customizable material properties. AM has also inspired the development of the maker movement by democratizing design and manufacturing. Due to the rapid proliferation of a wide variety of technologies associated with AM, there is a lack of a comprehensive set of design principles, manufacturing guidelines, and standardization of best practices. These challenges are compounded by the fact that advancements in multiple technologies (for example materials processing, topology optimization) generate a “positive feedback loop” effect in advancing AM. In order to advance research interest and investment in AM technologies, some fundamental questions and trends about the dependencies existing in these avenues need highlighting. The goal of our review paper is to organize this body of knowledge surrounding AM, and present current barriers, findings, and future trends significantly to the researchers. We also discuss fundamental attributes of AM processes, evolution of the AM industry, and the affordances enabled by the emergence of AM in a variety of areas such as geometry processing, material design, and education. We conclude our paper by pointing out future directions such as the “print-it-all” paradigm, that have the potential to re-imagine current research and spawn completely new avenues for exploration.
•The fundamental attributes and challenges/barriers of Additive Manufacturing (AM).•The evolution of research on AM with a focus on engineering capabilities.•The affordances enabled by AM such as geometry, material and tools design.•The developments in industry, intellectual property, and education-related aspects.•The important future trends of AM technologies.
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Exploring ultralight sandwich structures with superior load-bearing performance is one of the important topics in structural optimization. This paper proposes a novel multiscale topology optimization ...method to achieve the design of high-performance sandwich structures with graded cellular cores (SSGCCs). In this method, the thicknesses of two solid face-sheets, the graded distribution of cellular sandwich cores at a single layer and their configurations are optimized to well suit for loading conditions, where the single layer is arrayed periodically at its height direction to obtain sandwich layers. Specifically, at macroscale, the variable thickness sheet (VTS) method with the capacity of generating an overall free material distribution pattern, is applied to optimize the thicknesses of two solid face-sheets and achieve the graded distribution of cellular sandwich cores at a single layer. At microscale, a progressive optimization scheme is employed to topologically optimize multiple representative cellular cores (RCCs) at a single layer, so as to achieve their similar topological configurations. With a shape interpolation method, the configurations of graded cellular cores (GCCs) with essential interconnections can be obtained by interpolating the shapes of these RCCs with similar topological features. In order to reduce the computational burden on evaluating effective properties of GCCs by the homogenization method, a Kriging metamodel is constructed based on some key cellular cores as sample points, and adopted to predict the effective properties of all the GCCs. Both 2D and 3D numerical examples are provided to test the validity and advantages of the proposed method for designing SSGCCs.
•A novel multiscale optimization for sandwich structures with graded cellular cores.•A progressive optimization scheme with a shape interpolation method is proposed.•Two face-sheet thicknesses and spatially-varying cellular cores are optimized.•Several 2D and 3D numerical examples are presented to validate the proposed method.
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This article deals with the design of high-speed synchronous reluctance motors for electric vehicle applications. The need to enhance the power density and to lower the cost leads to research on ...high-speed motors with a reduced amount of rare earth. Pure synchronous reluctance motors potentially operate at high speed and exhibit a cost-effective rotor compared to permanent magnets and induction motors. Nevertheless, they present reduced performances in deep flux weakening operations, in particular when the so-called radial ribs are introduced to increase the mechanical robustness of the rotor. In this article, the introduction of the radial ribs and the related design challenges are investigated and discussed. The adoption of the topology optimization tool that is able to optimize the amount, the positioning, and the sizing of suitable structural ribs is presented. A design flow integrating the topology optimization is presented. The approach leads to an original positioning of the radial ribs able to preserve the performance of the motor at high operating speed enhancing the mechanical integrity of the rotor.
Phase-change materials (PCMs) excel in storing significant thermal energy through the latent heat of fusion during phase changes. However, they often suffer from low thermal conductivity, requiring ...the incorporation of materials with higher thermal conductivity to overcome this limitation. In this study, we employ the level-set method to topologically optimize the distribution of both PCM and high thermal conductivity materials within heat sinks.
The heat transfer process is modeled as an unsteady diffusion problem, with PCM integrated using the apparent heat capacity method. The finite element method, implemented using FEniCS, is utilized to compute the temperature distribution at each time step. The optimization problem is solved using ParaLeSTO, a modular topology optimization software written in C++, seamlessly interfacing with FEniCS through its Python interface.
To compute boundary point sensitivities for level-set topology optimization, the discrete adjoint method is employed, combining a perturbation scheme with automatic differentiation. The proposed methodology is first applied to a two-dimensional example of temperature oscillation minimization with a heat flux boundary condition, drawn from existing literature. Subsequently, a two-dimensional example with multiple volumetric heat sources is studied, followed by an extension to a three-dimensional design domain.
Comparisons with optimized designs without PCM, serving as a reference, highlight the superior thermal performance of heat sink designs with PCM. The results showcase a maximum temperature reduction of up to 42%, a mean temperature reduction of up to 42%, and a temperature variance reduction of up to 94%. This research contributes to heat sink design by offering discrete solutions that significantly improve thermal performance as compared to designs without PCM. Its impact extends to addressing crucial challenges in thermal management across various applications, including automotive cooling systems, aerospace components, and consumer electronics.
•Introducing level-set topology optimization for heat sinks with phase-change materials.•Comparative analysis between designs with and without phase-change materials.•Demonstrating method versatility with examples in two- and three-dimensions.
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We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which ...allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represent parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche’s method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero.
•A cut finite element method for density based topology optimization.•Complex design domain geometry on a structured computational grid.•Robust and flexible coupling between design and nondesign domain regions.•Independent discretization of parametric nondesign domain regions.
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This paper proposes a level set-based robust topology optimization (RTO) method for computational design of metamaterials under hybrid uncertainties, e.g. auxetics with negative Poisson’s ratio, ...where the Young’s modulus of the solid is described as a random variable while the Poisson’s ratio is regarded as an interval variable. Firstly, the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function. Secondly, the interval mean and interval variance are computed by a hybrid uncertain analysis approach, termed as Polynomial Chaos-Chebyshev Interval (PCCI) method. Thirdly, the design sensitivities of the robust objective function are obtained after the implementation of the PCCI method. Finally, a powerful parametric level set method (PLSM) in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure. Several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems. This method is non-intrusive and general, and can be easily extended to a range of design problems of micro-structured metamaterials.
•Level-set topology optimization method for auxetic metamaterials under hybrid uncertainties.•Interval and random variables accounting for the formulation of robust topology optimization.•Polynomial Chaos-Chebyshev Interval (PCCI) method for analysis of interval mean and variance.•Sensitivities of the robust objective function are obtained after the implementation of the PCCI method.•Parametric Level Set Method to achieve topological shape changes of the auxetic microstructure.
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Buckling-constrained structural design problems have conventionally prioritized optimizing the buckling load factor with less consideration given to the buckling mode shape. In this work, mode shape ...constraints are imposed within a topology optimization problem using an eigenvector aggregate constraint that is a weighted sum of homogeneous quadratic functions of the linearized buckling eigenvectors. A generalized formulation of the eigenvector aggregate is introduced, extending previous work. A new adjoint-based derivative evaluation technique is derived that is valid even in the presence of repeated eigenvalues. Numerical examples, including a clamped beam, a compressed column, and a square plate, demonstrate the effectiveness of the proposed approach. The results show the ability of the eigenvector aggregate to handle repeated eigenvalues, enable design space exploration, and capture mode shape switching.
•Eigenvector aggregates impose constraints on linearized buckling modal displacements.•Hyperbolic tangent generator function aggregates contributions from a range of modes.•Eigenvector aggregate derivatives are computed using a modified adjoint method.•Numerical examples demonstrate methods handle repeated eigenvalues and mode switching.•Designs optimized with the eigenvector aggregate may have better buckling performance.
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This study presents a unified formulation of topology optimization for finite strain elastoplastic materials. As the primal problem to describe the elastoplastic behavior, we consider the standard ...J2-plasticity model incorporated into Neo-Hookean elasticity within the finite strain framework. For the optimization problem, the objective function is set to accommodate both single and multiple objectives, the latter of which is realized by weighting each sub-function. The continuous adjoint method is employed to derive the sensitivity, which is a general form that accepts any kind of discretization method. Then, the governing equations of the adjoint problem are derived as a format that holds at any moment and at any location in the continuum body or on its boundary. Accordingly, the proposed formulation is independent of any requirements in numerical implementation. In addition, the reaction–diffusion equation is used to update the design variable in an optimizing process, for which the continuous distribution of the design variable as well as material properties are maintained. Two specific optimization problems, stiffness maximization and plastic hardening maximization, for two and three-dimensional structures are presented to demonstrate the ability of the proposed formulation.
•Topology optimization of finite strain elastoplastic materials is presented.•Proposed formulation is developed within the finite strain framework.•Objective function involves multiple objectives by weighting each component.•Continuous adjoint method is used for sensitivity analysis.•Reaction–diffusion equation is used to update the design variable.
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This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics ...and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. We describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.
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•A new topology-optimized fin pattern is generated for cold plate design.•Inverted TO fins derived, inspired by the wavy nature of channels with sectional fins.•Drop-oblique-trapezoidal and ...oval-shaped (DOTO) fins derived using inverted TO design.•DOTO fins reduced average junction temperature by ∼23% compared to TO design.•DOTO fins reduced the average junction temperature by 3 to 6 °C compared to benchmarked designs.
Direct-to-chip liquid cooling offers significant advantages in managing higher power densities compared to traditional air-cooling methods. This approach utilizes nearly half the power required by server fans and air conditioners, enhances cooling efficiency in data centers. The effectiveness of this cooling strategy is intricately linked to the layout of the cold plate fins. In this research, a density-based topology optimization method is implemented in generating free-forming and non-intuitive fin structures. A pseudo-optimization model, which approximates the 3D heat sink as two 2D thermally coupled problem is selected and optimized with ‘pressure drop’ and ‘average junction temperature’ as objective function and constraint, respectively. Several fin layouts with inlet flow velocities and temperature constraints are generated. Three-dimensional numerical simulations reveal that the average junction temperature with the topology-optimized fin pattern is ∼2°C higher, and the pressure drop is significantly lower compared to size-optimized straight channel. Building on this, an inverted topology-optimized design is introduced along the channel length, inspired by the wavy nature of sectional fins. The average junction temperature with the inverted TO design is 3 to 4°C lower compared to the straight design, with a similar pumping power of 0.023 W. The TO fin layout capitalizes on frequent re-initialization of boundary layers, secondary flow-induced mixing, and the formation of Dean vortices along the channel length. Further refinement leads to the derivation of drop-oblique-trapezoidal and oval-shaped (DOTO) fins. These fins reduce average junction and wall temperatures by ∼23% compared to the inverted TO design, owing to the persistent effects of fluid dynamic phenomena along the channel length. Comparison with benchmarked designs indicates that DOTO fins reduce the average junction temperature by 3 to 6°C compared to size-optimized offset strip fins and step fins, with a similar pumping power of 0.083 W. The study indicates that optimizing DOTO fins dimensions can further enhance heat sink performance.
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